Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 483 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 66 (d) 144
2. 2.In a class of 47 children, 29 like dance, 18 like music and 9 like neither. How many like both? (a) 8 (b) 9 (c) 10 (d) 38
3. 3.In a class of 56 children, 27 like tea, 28 like coffee and 9 like both. How many like only tea? (a) 28 (b) 19 (c) 18 (d) 27
4. 4.How many factors does 66 have? (a) 7 (b) 8 (c) 9 (d) 6
5. 5.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 513 (c) 514 (d) 504
6. 6.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 37 (c) 48 (d) 49
7. 7.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 6)(x + 9) (c) (x + 1)(x + 14) (d) (x + 1)(x + 54)
8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
9. 9.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 1 (d) 3
10. 10.What is the mean of 18, 3, 14 and 17? (a) 12 (b) 14 (c) 13 (d) 15
11. 11.What is the prime factorisation of 21? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
12. 12.In a class of 23 children, 15 like tea, 13 like coffee and 1 like neither. How many like both? (a) 6 (b) 22 (c) 1 (d) 5
13. 13.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 361 (c) 312 (d) 360
14. 14.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
15. 15.What is the mode of 7, 20, 6, 7, 7, 6 and 13? (a) 6 (b) 13 (c) 7 (d) 20
16. 16.How many factors does 114 have? (a) 6 (b) 8 (c) 7 (d) 9
17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
18. 18.In a class of 28 children, 13 like mangoes, 22 like bananas and 8 like both. How many like at least one of the two? (a) 28 (b) 19 (c) 35 (d) 27
19. 19.What is the distance between the points (6, 3) and (10, 0)? (a) 6 (b) 5 (c) 7 (d) 25
20. 20.How many prime numbers are there between 10 and 30? (a) 8 (b) 6 (c) 5 (d) 7
21. 21.In a class of 24 children, 17 like cricket, 14 like football and 9 like both. How many like at least one of the two? (a) 24 (b) 31 (c) 22 (d) 13
22. 22.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3731 (b) 3481 (c) 3721 (d) 3601
23. 23.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 840 (b) 420 (c) 456 (d) 68
24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
25. 25.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 27 (c) 8 (d) 72
26. 26.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 56 (c) 48 (d) 96
27. 27.What is the median of 16, 4, 10, 20, 5, 7 and 38? (a) 20 (b) 10 (c) 7 (d) 16
28. 28.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
29. 29.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 105° (d) 65°
30. 30.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 2)(x + 5) (c) (x − 2)(x − 5) (d) (x + 1)(x + 6)
31. 31.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 80°
32. 32.How many factors does 18 have? (a) 4 (b) 6 (c) 5 (d) 7
33. 33.A bag has 7 red, 2 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 2/17 (c) 2/15 (d) 15/17
34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
35. 35.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
36. 36.How many factors does 104 have? (a) 8 (b) 7 (c) 9 (d) 6
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
38. 38.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 55 (d) 22
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 1/11 (d) 5/36
40. 40.In a class of 46 children, 20 like maths, 20 like science and 2 like both. How many like neither? (a) 8 (b) 10 (c) 6 (d) 2

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